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The Myth Of Defensive Diminishing Returns

This was written before the Kotchman deal became public. I published it, then took it down when the Gutierrez news broke (so it wouldn’t get lost in the shuffle). This is not written to justify the Kotchman acquisition, which I’m lukewarm about. But it’s still true.

One of the popular phrases you’ll hear people spout is that the M’s “have enough” defense and now need to focus on adding some offense. The idea behind this is that adding another good defensive player will have less of an impact on the team’s overall record, because they are already a good defensive team. This is basically the theory of diminishing returns, where the next unit of something is worth less than the prior unit you acquired.

There are a lot of areas where diminishing returns are an important concept to understand. When stores try to up-sell you into an 84 ounce drink because its the best “value”, diminishing returns helps you realize that the actual value of the liquid beyond what you should consume is actually zero, so you’re paying for something you simply don’t need, and in reality, you should just order the human sized version.

This even applies in roster construction for baseball teams. The Mariners have four power right-handed relief pitchers on the roster right now, with David Aardsma, Mark Lowe, Brandon League, and Shawn Kelley. The marginal value of adding another reliever to the bullpen is diminished from their true talent level, because there are only so many high leverage innings to go around. If the team signed a guy like Jose Valverde, his innings would come at the expense of one of the relievers already here, so the actual value they’d get from Valverde would be less than what he would add to a team with a more shallow bullpen.

Since this is a valid theory, and it works in other parts of roster construction, a lot of people have no problem transferring it over to the defensive side of the game. The assumption is made that a quality defensive team will face diminishing returns from adding another quality defensive player, resulting in a value add that is less than the player’s actual abilities.

This assumption is wrong.

Put simply, almost every single ball in play that matters is only catchable by one player. On a line drive to left field, the quality of the defender at second base is completely irrelevant. That the team already has Franklin Gutierrez and Jack Wilson doesn’t matter when the hitter smashes a line drive down the first base line – the only variable on the defensive side is the quality of the first baseman. If he’s lousy, then the play isn’t getting made, regardless of how good his teammates are defensively.

Now, I know there are plays where two defenders converge on the ball, but those balls in play are going to be outs 99.9 percent of the time even if the second guy doesn’t get there. Even the worst defensive teams in baseball turn 65% of their balls in play into outs. Nearly two-thirds of all non-HR contact is fairly routine for the defense, and those plays are going to be outs whether you have Adam Dunn or Endy Chavez playing defense.

The plays that matter, though, where the runs are saved and wins are earned, are on balls that are smoked. Hot shots up the middle, sinking liners in the gap – this is where the difference in defensive ability comes into play, and on nearly all of those types of plays, there is only one guy who has a chance to convert the out. His defensive quality matters, and that’s it.

History has shown this to be true. When you put a good defensive SS next to a good defensive 3B, their individual numbers do not take a significant hit. Ichiro’s UZR did not go down when the Mariners replaced Jeremy Reed with Franklin Gutierrez, despite Death To Flying Things covering more ground than any outfielder in baseball. Adrian Beltre’s UZR didn’t crash when the team went from Yuniesky Betancourt to Ronny Cedeno and then to Jack Wilson. There just aren’t enough plays that matter where two guys both can convert the out for there to be significant diminishing returns in playing quality defenders side by side.

If the Mariners add a good defensive first baseman, they will get the full value from his glove, regardless of the fact that they already have good defenders around the field. If they upgrade their second base defense, it will improve the run prevention, even though they already have Jack Wilson playing shortstop. There is no evidence that there are significant diminishing returns from adding another good defender to a team that already plays good defense.

Run difference matters. Whether you create another 20 runs with an offensive first baseman or save another 20 runs with a defensive first baseman doesn’t matter. 20 runs are 20 runs, and those 20 defensive runs saved are not dependent on the skills of the other guys on the field.

Now, it’s certainly easier to find a +20 hitter than a +20 fielder at first base, so there’s a pretty solid argument to be made that the team will likely add a guy who is more of an offensive player at the position, but don’t buy into the hype that the team “needs a hitter and already has enough defense”. It’s not true.

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Comments

143 Responses to “The Myth Of Defensive Diminishing Returns”

Bodhizefa on
January 5th, 2010 12:26 pm

So Casey Kotchman is a good glove man, but he’s never really had much success hitting except in ’07. Is he going to be our solution at 1st now? I certainly think we can benefit from having a good glove at 1st base, but I’m also interested in getting the best overall player at this point. So good defense or no, please let us find the best all-around guy to help us win.

HeffMariner on
January 5th, 2010 7:38 pm

…doesn’t even mention that above average fielding at first base hides (or makes up for some) deficiencies elsewhere on the infield, and in fact makes them all better.

Sidi on
January 5th, 2010 7:41 pm

I could imagine it might be possible that there are actually increasing returns for defense on the infield.

It would probably be very slight, but I would think having good players at SS and 2B would not only make double plays go much more smoothly, but also lead to fewer mistakes in coverage and positioning.

All the infield positions have to work together to at least some degree, if they’re having to compensate for someone with less range or a weaker arm that has to compromise their game at least a little.

behappy on
January 5th, 2010 8:06 pm

And the run prevention gets better and better. Now Jack go get a #3 SP and the M’s will lead the league again in run prevention.

mfan on
January 5th, 2010 8:11 pm

Dave, your arguments seem be based on the fact that there is no diminishing marginal return with respect to additional defense’s effect on OBP. I think that can be true and it can also be true that there are diminishing marginal returns with respect to additional defense’s effect on runs allowed. Scoring runs usually requires stringing together several events that have a certain probability (namely, not getting out). So, the probability of scoring runs is multiplicative. For example, you must have a single and a double to score a run. Being so, the change in the probability of scoring runs is not constant as those probabilities increase/decrease.

I’m not doing a great job of explaining this. Consider a toy game with the following assumptions:

1. Each inning has one out.
2. Walks, singles and outs only.
3. Everyone on the team has the same OBP.

In this game, OBP rules, as it is the only thing that matters. The chances of scoring one run are OBP^4, as four positive events in a row must occur to score a run. The change in the probability of scoring a run with respect to a one point change in OBP is then 4*OBP^3. That is, the effect of changing OBP on the probability of scoring runs is higher the higher the OBP is.

So, just because the effect on OBP of additional defense doesn’t suffer from diminishing returns, we can not assume that the effect on runs is similarly unaffected. Defense, in it’s essence, lowers the opposing team’s OBP. If our defense is good enough that opponent OBP is already pretty low, that would suggest that lowering it even further would have a smaller impact on runs allowed than if the defense was mediocre to lousy.

MeanMachine on
January 5th, 2010 8:17 pm

Great post. The concept you are referring to is called the Law of Diminishing Marginal Utility and your conclusions are correct IMHO. 1st base was one of the very few defensive holes we have. 2nd/LF are the last spots where we are below average defensively. We are creating one of the best defensive teams in history.

Chris_From_Bothell on
January 5th, 2010 8:21 pm

The assumption is made that a quality defensive team will face diminishing returns from adding another quality defensive player, resulting in a value add that is less than the playerâ€™s actual abilities.

Not quite. It’s not about disbelieving that “a run saved = a run scored”. It’s a belief that “every team needs to score (unspecified minimum) runs”, as measured through high average, high RBIs, power numbers, etc. And concerns there get exacerbated when the traditional sources of that – the 3-4-5 hitters, the corner infielders, the corner outfielders – don’t produce that.

I’m not saying that people who obsess over powerrr hitting!!! and chicks dig the long ball!!! are correct. I’m just saying they’re not thinking about it the way you think that they think about it.

That’s a good point, mfan. The value of the outs saved will not be quite as high on a team that is good at preventing runners from reaching base. This would represent a diminishing returns situation.

In practicality, though, the effect will be very small for nearly every team. You’d have to combine both a great defense with a great pitching staff to start to reach the point where the value of the out was reduced significantly. The M’s probably have the latter, but I wouldn’t call this a great pitching staff. I don’t think this roster is particularly close to the extreme it would take for diminishing returns to kick in.

That said, your point is a good one.

Slurve on
January 5th, 2010 8:21 pm

2nd/LF are the last spots where we are below average defensively. We are creating one of the best defensive teams in history.

Lopez is a meh defender but nto really below average and Saunders is an amazing defensive outfielder.

daqmajor on
January 5th, 2010 8:34 pm

Wow! Great post, and mfan, solid response. You guys both know your economics, and at least mfan knows his calculus.

However mfan, while I think your point applies in the situation Dave described, it does not apply to first base. The reason here is that upgrading first base defense is the only position where upgrading improves the defense of more than one player, as improved 1B defense will affect all infielders performance. By upgrading to Kotchman, we improve the overall defense of the infield, and thus lower OBP by a much larger amount than if upgrading another position.

gag harbor on
January 5th, 2010 8:36 pm

The Kotchman trade seems like some other moves in that there are insider connections on the coaching/talent-evaluator staff that clearly the reason this is happening. Some of the same evaluators that thought Morrow was not worth as much also must think Kotchman is a good fit (at least he’s a lefty) for Safeco and a defensive-oriented 1B. Hope they are right and he breaks out this year.

We lose Hall as a sub in outfield… Does Kotchman play outfield at all? Maybe the flexibility that Z values so much is in regards to salary/years in this case. I guess I don’t think I’ll miss Hall all that much so I’m good with this move.

BLYKMYK44 on
January 5th, 2010 8:41 pm

I have a question I think is related to this…if you have two similar players but one is +20 runs on offense and one is +20 runs on defense would it be more beneficial to add the good defensive player to our already good defensive team? better to add the good offensive player? Or, does it still just cancel out?

camuskid on
January 5th, 2010 8:43 pm

Your argument that adding defensive prowess does not suffer from diminishing returns does not address the important fact that a team good at preventing baserunners will face fewer batters. Fewer batters means fewer opportunities for a given player to benefit the team by preventing runs.

For example, last year the M’s defense saved 85 runs according to UZR while the worst team defense (the Royals) gave up 50 runs. This is a differential of 135 runs. If I recall, each plate appearance is worth an average of ~0.12 runs, thus based solely on their respective defenses, the M’s would be projected to face 1100 fewer batters than the Royals. This is ~20% fewer batters faced! Because a defender playing for the Royals could expect to field ~20% more balls, the Royals would receive a greater marginal benefit from an equivalent defensive upgrade at a given position relative to the M’s.

daqmajor on
January 5th, 2010 8:46 pm

BLY,
Unless your team is extremely strong either offensively or defensively/pitching, it won’t matter. the value of runs saved = the value of runs scored for non-extreme conditions. When you start to have a superbly strong defense or a phenomonally strong offense, those values become slightly skewed. But since those situations are unlikely, just think that runs saved = runs scored.

Even then that’s not really the case if you take payroll into account, because tradition says players are paid more for offense than defense. So the player with +20 offense will be a much higher paid player (either through arbitration or FA) than the defensive player. But don’t worry about this last paragraph.

In addition to the situation that mfan described, there is another, albeit small, diminishing returns effect of adding defense. Lousy defensive teams provide each individual defender with more total chances than he would get on a great defensive team. In an extreme case, a great defender surrounded by 8 players who cannot create any outs will get at least 27 defensive chances a game. As the quality of the defense around him improves, the number of opportunities for him to flash the leather will decrease, hence his run prevention value will decrease.

However, as Dave pointed out, even the very worst defensive teams still turn 65% of the balls in play into outs, so this effect will be quite small, similar in size to the effect mfan described.

Rod O. on
January 5th, 2010 9:05 pm

As far as Kotchman playing other positions his career numbers are 465 games at first and 0 every where else but pinch hitter and dh.
One thing, not being as stat oriented as most at this sight, that came to mind as far a not getting diminishing returns from adding more defense. Wouldn’t adding more defense allow others around the new defensive oriented player be able to “cheat” position wise? Like if we added a top caliber defensive 2nd baseman couldn’t the 1st base man cheat a step toward the line. I would think that might help reduce diminishing returns. Just a thought I may be off target though.

kmsandrbs on
January 5th, 2010 9:18 pm

Would the reverse of mfan’s argument also point to a slightly higher return by adding offense to a point (or are we already at that point)? In addition, overall better offense leads to MORE offensive opportunities (the opposite of our diminishing opportunities with a better defense). Sure, I’m guessing, if there is a difference, it is incredibly small, but I’m still wondering.

mfan on
January 5th, 2010 9:37 pm

Would the reverse of mfanâ€™s argument also point to a slightly higher return by adding offense to a point (or are we already at that point)? In addition, overall better offense leads to MORE offensive opportunities (the opposite of our diminishing opportunities with a better defense). Sure, Iâ€™m guessing, if there is a difference, it is incredibly small, but Iâ€™m still wondering.

Sure. A team with an already high OBP will theoretically benefit more from an additional point of OBP added, all else equal, than a team with a low OBP. The only question is how large the effect is. Dave thinks the effect is small and I tend to agree, but that’s just my intuition. I think it might make a nice “tiebreaker” though.

Jake N. on
January 5th, 2010 9:44 pm

I am not overly crazy about this addition. Z is constant in players he aquires, defense and OBP are the prevailing tools he looks for. Last year we all saw what defense could do. This year an equally interesting test will take place. Can a team solely built with defense and OBP without the threat of HRs overcome the run differential we have struggled with the last 6 years. This team is looking more and more like Tampa Bay 2 years ago. Alot of running and gap hitting. Atleast it is going to be extremely fun to watch. Another solid Pitcher at this point would be real nice. Ben Sheets please.

thaduck30 on
January 5th, 2010 9:47 pm

Listen I love defense and pitching as much as anybody… I’ve always dreamed of putting together a Mariners team that took advantage of the ballpark by having guys that hit the ball in the gap and had speed and played great defense… But I do think we are undervaluing the importance offense just a bit.

What if Milton Bradley struggles? What if Jose Lopez has a down year? That is really all you have for guys that can drive the ball and bring in runs with extra base hits, who are consistently in the position of doing so. There isn’t anywhere close to a guy in our lineup that brings fear to the opposing team, or that a coach has to bring in a new pitcher to face by going to the bullpen that much sooner. To me, I feel like we’re going to get guys on base… but our success rate with RISP is going to be have to be huge.

As I see it, we have two great pitchers; Felix and Lee. There’s nothing close to a guarantee that RRS, Snell(especially), and whomever you slot into the 5th spot are going to be good enough to hold other teams to few enough runs for our power-depreived offense to consistently win. Our defense is good, but our pitching after the first two is no sure thing, and it can get out of hand real fast where we lose a lot of 2-1, 3-2 games. There just isn’t enough room for error. Build a team just like we are doing, with some great pitching, great defense, speedsters and high OBP guys, but build it around at least one guy whom at anytime can crack a 3-run jack in the 8th to save the game.

I was so high on Jack Z after the Lee deal, liked getting Milton for Silva, extending Guti and landing Figgins, and that can’t be ignored. But after inexcusably dumping Morrow for what we already had plenty of or could have gotten cheaper elsewhere, missing out on the affordable Nick Johnson and/or Harden and now acquiring Kotchman, I am convinced Jack Z is certainly nowhere near perfect.

I know this is going on forever. But if we don’t win this year… what happens? Lee will be gone. Felix might be here, and if he is, he’ll be uber expensive. And we’ll have tons of holes to fill with few draft picks or pieces to make any decent splashes that can fill all those holes. I think we are one big bat away from being the Phillies, I know that is saying a lot but I think it’s true. But we don’t have anyone near a Ryan Howard who can put us on his back when the others are slumping. But we’re just not doing it, and with how we’ve decided to go for it this year I just don’t get that.

With as close as I think we are, go above budget and splurge on a short-term high upside deal for Ben Sheets and really make the rotation deep and talented… or make the big splash we need to get a hitter who can compliment the excellent pieces we’d have to surround him.
Sorry again for the length

frankb. on
January 5th, 2010 10:04 pm

Thanks for this post and discussion. It’s let me see things in a different light. I often get my assumptions challenged by reading USSM.

LefebvreBelebvre on
January 5th, 2010 10:09 pm

Sidi nailed it.

Dobbs on
January 5th, 2010 10:16 pm

Thanks Dave and mfan for covering the thoughts running through my head on the exception to Dave’s post. I figured it was a bit nit-picky since the situation is small, but it’s always good to cover all bases:)

wschroer on
January 5th, 2010 10:24 pm

Sure. A team with an already high OBP will theoretically benefit more from an additional point of OBP added, all else equal, than a team with a low OBP. The only question is how large the effect is. Dave thinks the effect is small and I tend to agree, but thatâ€™s just my intuition. I think it might make a nice â€œtiebreakerâ€ though.

Actually, isn’t exactly the opposite the case? A team with a low OBP would theoretically gain more by adding one point of OBP than a team with a high OBP, since the formula (OBP+.001)/OBP would yield a larger number for a lower OBP, thus a more significant percentage increase.

O

Leroy Stanton on
January 5th, 2010 10:35 pm

I probably wouldn’t have myth in the title, but you’re right, there probably aren’t enough situations to make it significant.

However, there are several common situations where this could apply. A Texas-leaguer, where an OF or middle infielder could make the play, a ground ball in the hole between SS/3B or 2B/1B, or a foul popup to the 3B/SS or 1B/2B. These are not 1 in 1000 type occurrences. But still, probably not worth losing sleep over.

mfan on
January 5th, 2010 10:39 pm

Actually, isnâ€™t exactly the opposite the case? A team with a low OBP would theoretically gain more by adding one point of OBP than a team with a high OBP, since the formula (OBP+.001)/OBP would yield a larger number for a lower OBP, thus a more significant percentage increase.

That’s just the formula for the percentage change in OBP and, yes, a one point change in OBP is a larger percentage change the smaller the initial OBP is. However, that’s not what I’m referring to. I’m talking about the effect of increased OBP on runs scored. As a theoretical example, consider a team that goes from .999 to 1.000. Their runs scored go from something large but finite at .999 to infinity at 1.000, an infinitely large change. However going from, say, .001 to .002 will have a smaller, finite effect. The effect gradually increases over the range. Within the reasonable range for MLB OBP, the change in value of increasing team OBP (or some other better metric) is probably pretty small.

schachmatt on
January 5th, 2010 10:53 pm

I have a couple questions.

Is there a quantified effect that a good defensive first baseman has on the defensive statistics of the other infield positions? My first thought is that an agile defensive first baseman would be a significant benefit to the other infielders by cutting down on the number of throwing errors assigned to them by picking balls or applying tags when pulled of the bag that average first baseman wouldn’t make. If true, this would be another arguement against diminishing returns of defensive skills.

On the subject of +20 runs offensively vs + 20 runs saved defensively being about equal or runs saved = runs scored (per daqmajor in an earlier post); would saved runs be more valuable over the course of a season due to the increased mileage the team would get out of the same pitcher’s arms (fewer pitches for the same number of outs)?

wschroer on
January 5th, 2010 10:55 pm

thaduck30 said

But I do think we are undervaluing the importance offense just a bit.

I couldn’t agree with you more. It is almost like there is a fog of forgetfulness around what the successful Mariner’s teams have looked like in the past, and what the championship teams of most years looks like.

It was not that long ago that the Mariner’s set the single season record for most runs in a season. What did that team look like offensively? Anything at all like this team? And that team also played in Safeco Field, the supposed stadium that makes success with right-handed batters impossible.

Brett Boone, a right handed batter hit 37 home runs that year – 19 in Safeco and 18 on the road. I am not denying that Safeoo can be tough on right handed hitters, but it is tough on both teams. Do yourself a favor – go look at the stats of that 2001 team and ask yourself if you think there is anyway the current team could even hold a rather dull, windblown dim candle to that team.

This team just does not have the horses. That team had 4 quality guys to hit middle of the order – Cameron, Edgar, Olerud, Boone. Don’t you think we need at least one quality middle of the order bat to have a prayer to be successful?

Blah blah blah. You wouldn’t have liked the 2001 offense before the season then either.

You guys and your “we need offense” crap have opinions and nothing else. It’s old. Find some evidence to support your theory or consider that you might be wrong.

wschroer on
January 5th, 2010 11:03 pm

However, thatâ€™s not what Iâ€™m referring to. Iâ€™m talking about the effect of increased OBP on runs scored.

But at the other end of the spectrum of your example, let’s say a team has one base runner all year, and pretend with 1000 ABs, an OBP of .001. Should they get their 2nd base runner they have now doubled the opportunities to score by simply increasing their OBP by .001. Perhaps it would be fair to say that if a team has a high OBP, adding a point might result in a higher aggregate of runs scored, but a team with a lower OBP would benefit more as a percent of increase in offense.

wschroer on
January 5th, 2010 11:12 pm

[blah blah blah]

Chris_From_Bothell on
January 5th, 2010 11:17 pm

You wouldnâ€™t have liked the 2001 offense before the season then either.

Actually, that’s an interesting perspective. Here’s some of the ‘traditional’ stats from the 2000 season, for some of the core of that 2001 team:

and A-Rod had just left, and we were bringing in some weird slap hitter from Japan.

CCW on
January 5th, 2010 11:18 pm

I totally agree with Dave, here. People in the “we need a power bat” camp have been given every opportunity to explain why a run scored is any more valuable than a run saved, and no one has come up with anything.

Now, it’s true the M’s probably won’t be among the league leaders in runs scored in 2010. In fact, the offense may not be very good at all. But that’s not the same as saying the team won’t win a lot of games. This is going to be an incredibly fun team to watch, and they’ll probably win enough games to compete in the AL West, too. I’m excited.

They can’t do it because they don’t know what they are talking about. So they ramble. It’s sad.

SequimRealEstate on
January 5th, 2010 11:23 pm

@Schachmatt
look up the effect that John Olerud had on the teams feilding when he moved to a new team. I think the answer is yes.

wschroer on
January 5th, 2010 11:31 pm

You wouldnâ€™t have liked the 2001 offense before the season then either.

Actually 2001 was the last year I partnered up to buy season tickets. I was quite optimist about that team. What a dope I was, thinking that a powerful offense might produce some wins.

mfan on
January 5th, 2010 11:35 pm

But at the other end of the spectrum of your example, letâ€™s say a team has one base runner all year, and pretend with 1000 ABs, an OBP of .001. Should they get their 2nd base runner they have now doubled the opportunities to score by simply increasing their OBP by .001. Perhaps it would be fair to say that if a team has a high OBP, adding a point might result in a higher aggregate of runs scored, but a team with a lower OBP would benefit more as a percent of increase in offense.

Nah, it has a larger percentage effect on OBP, but not a greater effect on runs scored. I’m certain what I’m saying is correct and have already explained it as best I can without writing an essay, so I’m going to avoid spending more space explaining further.

Chris_From_Bothell on
January 5th, 2010 11:36 pm

People in the â€œwe need a power batâ€ camp have been given every opportunity to explain why a run scored is any more valuable than a run saved, and no one has come up with anything.

Because it’s the wrong argument to have. The “we need a power bat” camp believes there’s a minimum amount of offense needed at all, especially from whoever is batting 3rd, 4th or 5th in the lineup. Because all the superstars – all the big names – all the sluggers – tend to be slotted there. So anything less than a murderer’s row of fearsome hitters for the middle of the order, and the sky’s falling.

Or, the opposite of results-based analysis – e.g., the theory that you could build a team of roughly equal OBP guys and bat them in any order has solid math behind it, but no real-world example teams to point to, so it gets dismissed.

I’ll bet you the powerrr hitting!!! crowd looks at this and says “no playoff-caliber team scores less than 750 runs”. And the “run saved = run scored” crowd sees something closer to “if your team’s on track to score 100 – 120 runs more than it allows, you should be fine”.

Leroy Stanton on
January 5th, 2010 11:40 pm

Dave,

I’m surprised you don’t like the Kotchman deal more. Especially considering your post on first base options. Don’t you consider Kotchman, all things considered, on par with Overbay or LaRoche?

thaduck30 on
January 5th, 2010 11:42 pm

[bye]

Bandit24 on
January 5th, 2010 11:48 pm

The reason here is that upgrading first base defense is the only position where upgrading improves the defense of more than one player, as improved 1B defense will affect all infielders performance.

I disagree. It is not the only position that improves the performance of more than one player. How many times have you seen a second baseman or shortstop pick a ball thrown down to second by the catcher? It happens quite a bit….

Gibbo on
January 5th, 2010 11:52 pm

why a run scored is any more valuable than a run saved, and no one has come up with anything

I am sure I am not the first person to ask this question… but here goes.

I would think that the one reason a run scored is more important than a run saved is that at the end of the day you cant win a game 0 to -1. So surely a run scored at the point a game is tied with no score then that run scored eventually has more value – doesnt it?

I understand that saving the runs keeps you in games but you do need to score too.

TumwaterMike on
January 5th, 2010 11:52 pm

Does anyone remember when the M’swon 116 games. they had the best defense in the American league that year. That was due in part because John Olerud played first. His defense was essential as Carlos Guillen would be erratic on his throws to first at times and Olerud fielded the position so smoothly that it didn’t seem to matter. I think 1B defense is very important.

I would think that the one reason a run scored is more important than a run saved is that at the end of the day you cant win a game 0 to -1. So surely a run scored at the point a game is tied with no score then that run scored eventually has more value â€“ doesnt it?

Every time I think this argument can’t get lower, someone breaks out a larger shovel.

I think defense is more important, because if both teams score an infinite amount of runs, the one that reduces the other team’s score will win infinity to (infinity-defense contribution)

Liam on
January 6th, 2010 12:00 am

Do yourself a favor â€“ go look at the stats of that 2001 team and ask yourself if you think there is anyway the current team could even hold a rather dull, windblown dim candle to that team.

If the 2001 club went 85-77, they still would have made the playoffs. Any team will look poor in comparison to the 2001 Mariners, but sometimes a 90 win imitation works just as well.

wschroer on
January 6th, 2010 12:21 am

We don’t need a power bat.

We need multiple power bats. One power bat is someone to pitch around. Multiple power bats create situations which result in 141 RBIs for Boone, 116 RBIs for Edgar, 110 RBIs for Cameron and 95 RBIs for Olerud.

Okay okay okay. RBIs are meaningless. They are a reflection of the situations the players find themselves in, not the talent of the players. But what happens when good offensive players bat one after the other? RBIs result. It is a cummulative effect. That is why build a great defensive team will NEVER be as effective as building a great offensive team.

Great offensive teams allow there to be a build up – a accumulation of effect of having great hitters follow each other. Defensive plays are made in isolation mostly.

The fallacy of most of the current fielding superstats and WARs is that they only make sense if you view every baseball event in isolation. But great offenses are not isolated events of batters facing pitchers. The hitters that came before and the hitters yet to come, as well as the current situation all contribute to what will be seen on the next pitch. Great offensive teams mean that a hitter’s success is not an isolated event, but is more likely to either drive in a previous batter, or sets the stage so the next hitter’s success will be more valuable because it happens with runners on base.

I do not think that defense should be ignored or minimized. But it cannot be the main focus of a championship team, because, though it sounds cliche, a championship team is greater than the sum of its parts, and just as your article pointed out, adding good defense may not have diminishing returns, but adding offense has increasing returns.

How is adding 20 runs better than preventing 20 runs? It isn’t of course.

But if you take a guy who adds 30 runs, and bat him behind a guy that adds 30 runs, and then put another guy behind him that adds 30 runs what actually happens is that all of the guys end up producing 40 or 50 more runs because of the situations they find themselves in. Exam almost any championship team and you will see this pattern.

1993 Toronto – Carter 121, Molitor 111, Olerud 107, Alomar 93.

1998 NYY – Tino 123, O’Neil – 116, Williams 97

1977 NYY – Jackson 110, Nettles 107, Munson 100, Chambliss 90

You can find a team from time to time that didn’t have a clot of sluggers in the middle – 1968 Cards, 1969 Mets… but look at the pitching rosters of those teams…..Nolan Ryan as a spot starter…? Steve Carlton as your number 3 starter? These teams that have been champs have had great, i.e. mostly HOF staff. Do we really think we have that here? We have a great top of the rotation, but no one who will be renown as a Tug McGraw or Nolan Ryan as bullpen guys.

Why is offense a better way to go? Because your efforts accumulate. Simple as that.

His (Beltre’s) lateral range is hilarious at times, as he regularly fields balls that are hit directly at the shortstop, just because he can.

Funny how you could write that one day and the very next day write this post.

wschroer on
January 6th, 2010 12:35 am

I think defense is more important, because if both teams score an infinite amount of runs, the one that reduces the other teamâ€™s score will win infinity to (infinity-defense contribution)

Infinity minus 1 is still infinity.

Your theory ignores how offense works. I would argue that a theoretical Ichiro is a more productive player when followed by Edgar, compared to a theoretical Ichiro followed by Al Martin.

Offense accumulates faster and declines more rapidly then the addition of the individual player’s contributions.

CCW on
January 6th, 2010 12:37 am

Leroy, think about it. If the ball’s hit directly to the shortstop, then the defensive ability of the shortstop doesn’t matter. You can’t have dimishing returns. This just reinforces Dave’s point: it’s very rare for a ball to be hit where two great defenders (but only great defenders) can get to it, such that one defender’s talents are “wasted” and you reach a point of diminishing returns.

Gibbo on
January 6th, 2010 12:42 am

I think defense is more important, because if both teams score an infinite amount of runs, the one that reduces the other teamâ€™s score will win infinity to (infinity-defense contribution)

OK totally get that part but would the M’s strong D be enough to outweigh say the strength of a Yankees offense? I guess what I am trying to understand is, does having the best D in the majors outweigh having an average offense? Is there a formula that values one more than the other?

Dont get me wrong, I really like the way we are building this team, but am just playing dveils advocate a bit and trying to understand the value of one vs the other.

CCW on
January 6th, 2010 12:47 am

Mr. Wschroer, I’ll give you that your argument makes enough intuitive sense that I can finally understand where you’re coming from, but you’re still wrong. You take the WAR of the 2009 Yankees and it still adds up to their approximate number of wins. Same with the 2009 Mariners, even though one team’s offense was great and the other was anemic. The cumulative effect you’re talking about may sound good to you in theory but it isn’t real in practice. Hopefully, someone better versed in this than me will come along and explain this further, and hopefully you’ll be willing to learn.

CCW on
January 6th, 2010 12:53 am

Gibbo, I think the answer to your question is that no, you can’t get all the way there with defense, because even the very very best defenders, at premium defensive positions, can only add 3 or 4 wins with their glove. You just can’t get enough wins out of great defense alone to be a great team. You could get there with run prevention in general, though (i.e. pitching + defense). Certainly an average offense + stellar run prevention could produce a championship caliber team. Take the 2009 M’s. Even with just so-so pitching, with the awesome defense, if their offense had been league average rather than in the bottom quartile, they’d have won 90 games.

Haha Dave you seem particularly harsh today. I’m in the “run saved=run scored” boat, but I also kind of wonder whether a “run saved > run scored.”

By running out an MLB best defense and preventing runs from crossing the plate, you can take an average-ish pitcher like Jarrod Washburn and give him a sparkling ERA around 2.75 and then dupe another GM into thinking Washburn is better than he actually is. So then doesn’t having a stellar defense increase the apparent value of your pitching staff?

Or does my assertion just assume every other GM is Bavasi-esque and does not project the pitcher’s performance to their defense?

Leroy Stanton on
January 6th, 2010 12:55 am

@CCW

Put simply, almost every single ball in play that matters is only catchable by one player.

Any ball hit directly at the SS where a 3B is able to get to it will be hit softly enough to make it a difficult play for the SS. The faster the runner, the harder the play. When Ichiro hits this ball, for instance, it’s usually a single.

mfan on
January 6th, 2010 12:58 am

Offense accumulates faster and declines more rapidly then the addition of the individual playerâ€™s contributions.

If you accept this logic, wouldn’t you also have to accept the same logic with respect to limiting the other team’s offense?

Leroy Stanton on
January 6th, 2010 1:08 am

If you accept this logic, wouldnâ€™t you also have to accept the same logic with respect to limiting the other teamâ€™s offense?

To an extent – you can’t defend against a walk, for instance.

PCS_eagles on
January 6th, 2010 1:08 am

Okay, mostly agree with the idea that improved defense is just as valuable as improved offense, therefore the M’s don’t necessarily need to improve offense (translate: get a “big bat”). However, I’d like to see Dave’s input on how two factors affect the scenario.

1st factor: Pressure. A team with little but great defense might find itself in close games more frequently than one with a great offense. How does the resulting accumulation of “pressure innings” affect the analysis?

2nd factor: Length of innings. A team with great offense would tend to make a pitcher throw more pitches by putting runners on base more often and having fewer short innings. Great defense would conversely tend to shorten innings by getting people out. Are these a wash, or does one of the two create an advantage over the other? I believe it is usually considered an advantage to make the opponent’s starting pitcher throw more pitches, thus getting into the bullpen faster. Are there statistics to support this impression that I have? And furthermore, is great defense or great offense more likely to affect pitch count?

youarelikeme on
January 6th, 2010 1:17 am

Could it not also be argued that adding a defensive specialist at first base would increase the defence of all the other players on the infield.
The reason being that say a shortstop for example would be more inclinded to make a difficult throw because he has faith that his first baseman would be able to bail him out if the throw went wild.
I think that one of the most recent examples of that would be the improvement of Jeter with the addition of Teixeria.

LB on
January 6th, 2010 1:25 am

> Whether you create another 20 runs with an offensive first baseman or save another 20 runs with a defensive first baseman doesnâ€™t matter. 20 runs are 20 runs

Actually, if you do the Pythagorean math, you do a bit better subtracting 20 from RA than you do adding 20 to RS.

CCW on
January 6th, 2010 1:30 am

Any ball hit directly at the SS where a 3B is able to get to it will be hit softly enough to make it a difficult play for the SS.

The universe of balls in play where only an above average 3B could make the play AND only an above average SS could make the play on the same ball is very very very small. Go back and watch all of Beltre’s great plays in that video over the past 5 years. How many of them both (a) would not have been made by an average 3B and (b) would have been made by great defensive SS but not an average defensive shortstop? 0. Maybe 1, if you assume it was Ichiro who hit the ball. Maybe I’m missing something, but that part of Dave’s point seems almost irrefutable to me.

nyc mariner on
January 6th, 2010 1:47 am

Dave’s argument in general makes intuitive sense to me. However, even if a defensive squad could turn every ball in play into an out, it still could not defend against walks, hit-by-pitch, or homeruns. Once the ball leaves the pitcher’s hand, the defensive squad is at the mercy of the batter’s prowess. That is why, no matter how great my team’s run prevention is, I feel much more secure if it is capable of scoring a few runs for a come-from-behind win.

Leroy Stanton on
January 6th, 2010 2:07 am

@CCW

I think maybe you should re-read what I said. I didn’t refute Dave’s point – in fact, I conceded it in an earlier comment.

Maybe Iâ€™m missing something, but that part of Daveâ€™s point seems almost irrefutable to me.

I can tell by your spirited defense of Dave, that a lot of his points are irrefutable to you.

This particular post of Dave’s is not filled with a lot of in-depth analysis. I happen to agree with it, but it’s basically him declaring things that he believes to be true, not necessarily things he has any evidence for. Even when he does offer evidence, it is half-hearted and weak, and he would have had a field day with it if it had been offered to him instead of by him.

So, we can all just say something is very, very, very small and watch videos and make up numbers like 99.9%, but that’s not evidence, it’s just opinion.

CCW on
January 6th, 2010 2:47 am

I can tell by your spirited defense of Dave, that a lot of his points are irrefutable to you.

It’s late, so maybe that’s the problem, but even with (especially with) your emoticon, that pisses me off. I’ve had more than my share of knock down drag out battles with Dave in these comments, and to suggest I’m some sort of obsequious lap dog (of which there are a few around here) is offensive.

I also disagree with your assessment of the post. Not every statement or discussion needs to be grounded in quantitative analysis to be important, or interesting, or correct. Dave’s post, and mfan’s response are a perfect example of good theoretical discussion of a concept that would be very difficult to quantify directly.

jouish on
January 6th, 2010 2:48 am

@wschroer

Infinity minus 1 is still infinity.

He was pointing out the absurdity in the referenced argument, not making a serious argument.

As for your argument about increasing returns, it’s false. I’m assuming when you say “adding 30 runs” you’re referring not to RBIs, but to something like wRAA. Those are contextualized values and do not stack with each other to amplify the effect.

If you’re referring to RBIs then you’re basing your entire argument on something that you said is a meaningless stat. Try again.

A simple test. Add up the projected runs scored from “good” offenses based on whatever RC formula you want to use. If what you say is true then the RC formula will consistently be lower than the actual runs scored for the team that year (if you want to save yourself the work, you can take my word for it that it doesn’t). You can even use “bad” offenses as a control.

terry on
January 6th, 2010 5:18 am

This is an awesome post and there are are a lot of little nuggets buried within it that are food for thought…enough so to make the brain obese…

Paul B on
January 6th, 2010 7:03 am

would think that the one reason a run scored is more important than a run saved is that at the end of the day you cant win a game 0 to -1. So surely a run scored at the point a game is tied with no score then that run scored eventually has more value â€“ doesnt it?

Perhaps (and I’m trying to understand the thinking that lead to this discussion) the problem is the idea that there is a minimum offense and it is zero runs scored.

That isn’t true, because no team is going to run out players that are worse than replacement level, and even a team of replacement level hitters are going to score some runs.

rmnixon on
January 6th, 2010 7:43 am

[see you!]

Chris_From_Bothell on
January 6th, 2010 7:51 am

CCW:

Take the 2009 Mâ€™s. Even with just so-so pitching, with the awesome defense, if their offense had been league average rather than in the bottom quartile, theyâ€™d have won 90 games.

Paul B:

and even a team of replacement level hitters are going to score some runs.

So is it fair to say the 2010 Ms are being constructed the same way as 2009 – superior pitching and superior defense means that you can assume that a) an average offense will be sufficient and b) an average offense will show up (which is, semantically speaking, kind of the definition of average in the first place)?

Or put another way: the offense being close to last in the majors in many categories in 2009 was an exception to the rule and not likely to repeat. Therefore, it’s not important to seek out players with superior offense, or to have bats available on the bench that will provide more than replacement-level offense when others slump. The offense won’t be nearly as bad as 2009, so you can try the same basic approach again.

Chris_From_Bothell on
January 6th, 2010 7:53 am

Corollary to last point: This means the Ms are free to seek out whoever provides the best market value for a particular position this offseason, because they don’t have to “pay for” offense.

snapper on
January 6th, 2010 8:28 am

I think the issue simply stated is that while there are not diminishing returns to defense, there are increasing returns to offense (OBP in particular). Good hitter make fewer outs, giving their teamates more chances to generate runs.

One analysis of the Nick Johnson signing (RLYW) showed that he would produce ~20 R’s with the bat, and allow his teamates to produce another ~5 R’s b/c he makes so few outs.

One problem that I see with this concentration on defense is that it will result in low scoring games. Weâ€™ll be at the mercy of die throws when it comes to 1 run results.

Last year the Mariners were 35-20 in one run games (by contrast the Yankees, with the best record in the league, were 22-16 â€“ they were involved in 17 fewer 1 run games). My feeling is that these games are pretty much 50/50 propositions and we could just as easily have been 20-35 (a 70-92 season â€“ imagine how weâ€™d be feeling about the front office in that caseâ€¦). And certainly 28-27 in these 55 games (resulting in a 77-85 season and very close to the Mariner pythag of 75-87) would seem well in the realm of possibility.

I once heard that good teams donâ€™t necessarily win the 1 run games â€“ they win the 5 and 6 run games. I donâ€™t know that this Mariner team is built to win many 5 or 6 run games.

Unless the Mariners have some sort of secret weapon that makes one run games a winning proposition again this year, Iâ€™m a bit worried that we wonâ€™t be as lucky in them in 2010 as we were in 2009. The answer, in my mind, is to score more runs and avoid relying on Lady Luck.

wschroer on
January 6th, 2010 8:39 am

Mr. Wschroer, Iâ€™ll give you that your argument makes enough intuitive sense that I can finally understand where youâ€™re coming from, but youâ€™re still wrong. You take the WAR of the 2009 Yankees and it still adds up to their approximate number of wins.

Of course WAR relates to the number of wins on a team, because it is a derivative stat.

wschroer on
January 6th, 2010 8:41 am

Sorry, screwed up the bquote on the last one, should be flipped

Jeremariner on
January 6th, 2010 8:55 am

I agree with the premise of this analysis, but isn’t there also something to be said for the accelerating returns of a well-structured and balanced offense? The fact that defensive positions are isolated on the field prevents much accelerated return on defense (except maybe for pitcher stats), but on offense, each player’s run production depends primarily on the guys who bat before and after him.

That being said, a good defensive 1B who can dig low throws out of the dirt could give us some good accelerated return…

So I still contend that while another good defensive position won’t necessarily have diminished returns, at least one more offensive bat is probably still needed to provide that little bit of accelerated return that will boost our team into contention.

Where is the evidence for this accelerated return which exists on offense but not on defense?

Chris_From_Bothell on
January 6th, 2010 9:11 am

Where is the evidence for this accelerated return which exists on offense but not on defense?

What would you accept as permissible evidence?

Leroy Stanton on
January 6th, 2010 9:15 am

Where is the evidence for this accelerated return which exists on offense but not on defense?

Where is the evidence against defensive diminishing returns?

Alex on
January 6th, 2010 9:16 am

Thatâ€™s a good point, mfan. The value of the outs saved will not be quite as high on a team that is good at preventing runners from reaching base. This would represent a diminishing returns situation.

Yes this is a great discussion and very interesting. I would agree with Dave that the effect is minimal. We are talking about reducing OBP by about .00x for each of these defensive upgrades.

Another counterbalancing factor is that as you reduce runs scored, the value of each extra run prevented increases.

We normally assume that about 10 runs (prevented or scored) is equal to a win, but in lower scoring environments that number decreases somewhat. Thus, while a defensive upgrade might end up preventing only 9 runs instead of 10 due to the effect you listed, this might still be worth about the same 1 win. I’m not saying that this effect exactly counteracts the effect, but it at least partially counteracts it.

The person making the claim needs to supply evidence. It’s a basic tenet of science and beyond that, quality reasoning. I don’t have to disprove that there’s an invisible dragon that lives under your bed. I think this is discussed in the comment guidelines, in fact.

HubofPNW on
January 6th, 2010 9:37 am

I am a couple decades removed from calculus and can agree with this post in a vacuum, but with THIS particular roster and with such a great opportunity to produce offense batting behind Ichiro and Chone, is there any way to measure how much production differential putting an Adrian Gonzales behind those two vs the top 1B defender? I just think that that an adequate 1B defender that is superior at the plate in the 4 or 5 hole for THIS team would produce more runs than an adequate bat/superior defender would save.

Leroy Stanton on
January 6th, 2010 9:39 am

The person making the claim needs to supply evidence. Itâ€™s a basic tenet of science and beyond that, quality reasoning. I donâ€™t have to disprove that thereâ€™s an invisible dragon that lives under your bed.

DMZ,

Don’t we know instinctively that a team with 20 hits/walks in a game will score ~10 runs, while a team with 5 hits/walks will score ~1? It would be simple enough to show with access to game data, but I think everyone accepts it as self-evident.

Now, I know there are plays where two defenders converge on the ball, but those balls in play are going to be outs 99.9 percent of the time even if the second guy doesnâ€™t get there.

or

The plays that matter, though, where the runs are saved and wins are earned, are on balls that are smoked. Hot shots up the middle, sinking liners in the gap â€“ this is where the difference in defensive ability comes into play

or

There just arenâ€™t enough plays that matter where two guys both can convert the out for there to be significant diminishing returns in playing quality defenders side by side.

are just statements that aren’t backed up with any evidence. It’s all well and good to say you need to supply evidence, but the reality is that even the best of us sometimes simply resort to common sense or intuition when making an argument.

Good post. All things being equal, if anything a good (over .500) team like the Mariners would actually benefit more from run prevention (pitching and defense) more than hitting. Of course you want to maximize both, but given the choice run prevention will improve a good teams pythagorean record more than more runs scored (given that they are the same amount +-). The difference may not be all that big, depending on how many runs prevented vs runs scored you are talking about, but it’s a difference nonetheless.
[]

Chris_From_Bothell on
January 6th, 2010 10:04 am

I donâ€™t have to disprove that thereâ€™s an invisible dragon that lives under your bed.

No one in the powerrr hitting!!! chicks dig the long ball!! camp asks for that.

The person making the claim needs to supply evidence.

Again: What qualifies as permissible evidence?

Is there a specific formula based on hits, runs, OBP, SLG, OPS, OPS+, etc. that is going to be convincing? Are there specific trends, derived from specific minimum sample sizes, that would be convincing?

RBIs aren’t valid (for logically obvious reasons). Clutch isn’t valid (any more than unicorns are, because neither exists). What kind of evidence do you need, in order to be persuaded that there’s a specific minimum level of offense needed in order to be playoff caliber team?

I’m honestly not trying to play semantics games, I’m trying to help. (You know me on here, I’m not some random troll.) It’s hard for the person with the burden of proof to supply evidence when at many turns it’s just rebuffed with “that’s just your opinion”.

Paul B on
January 6th, 2010 10:35 am

What would you accept as permissible evidence?

I don’t think permissable is the word you were going for, there.

Maybe satisfactory, or perhaps acceptable, or even sufficient.

FrankTheTank on
January 6th, 2010 10:35 am

Not sure I buy this, wholly. A couple of thoughts.

1. The fact that there is a natural limit to the number of runs the defense can save would imply that defense is something with declining marginal utility. That is, at the limit, even the best defense possible cannot prevent every run, and thus runs saved is asymptotic.

Now, you can claim, that no team is close to this “perfect defense” and thus we don’t approach the point of diminishing returns on defense, but that’s difficult for me to believe.

Alternately, you can suggest, as someone did above, that the value of each marginal saved run is increasing and thus despite the fact that there is a diminishing return on incremental defense from an actual runs saved perspective, the “value” is not diminished. But that’s not what you’ve claimed here.

2. I’m not sure UZR is the right basis for analysis. I’ll agree that UZR would only be affected minimally with defensive additions (for the reasons you note), the fact that there are a limited number of “savable runs” suggests that it’s incomplete. Which I guess gets back to my first point.

Paul B on
January 6th, 2010 10:41 am

Now, you can claim, that no team is close to this â€œperfect defenseâ€ and thus we donâ€™t approach the point of diminishing returns on defense, but thatâ€™s difficult for me to believe.

Why is that difficult to believe?

Can you point to a defense that is close to perfect? I would expect that perfect defense to turn every ball in play (except for home runs) into an out. Where is that team?

Chris_From_Bothell on
January 6th, 2010 10:44 am

I donâ€™t think permissable is the word you were going for, there.

Maybe satisfactory, or perhaps acceptable, or even sufficient.

Decent point. How about just “good”. What would be good evidence that there’s some minimum amount of offense necessary to be a playoff-caliber team?

jouish on
January 6th, 2010 10:46 am

Donâ€™t we know instinctively that a team with 20 hits/walks in a game will score ~10 runs, while a team with 5 hits/walks will score ~1? It would be simple enough to show with access to game data, but I think everyone accepts it as self-evident.

That argument then goes both ways. Each hit/walk saved on defense would result in accelerated returns.

RBIs may be a poor measure of an individual’s contribution, but it seems that the prima facie evidence is that it is a valid measure of the value of a batter in an offensive system – the value of being surrounded by other productive offensive players. It does reflect how often runners are on base prior, at what base, as well as the number of outs (less than 2 means a SF/SB is a possibility.) It is not an indifferent stat. Is Mike Cameron a 100 RBI guy? Yes, if snuggled up next to Edgar, Olerud, Boone in 2001, he was. He is a decent offensive asset who’s value is significantly increased when serial used with other positive offensive assets. Throw him into a lineup with other lesser talents, his production is kinda okay – K’s a lot, hits a few out. But when he is the guy that is at the plate after the opposition has tiptoe’ed past Edgar and Ollie and Boone – well, they have to pitch to someone, don’t they? More likely someone is on, so whatever he does will likely be more productive….. resulting in more RBIs.

I buy the basic premise that adding good defense does not result in diminishing returns – that it is truly a additive function, but posit that adding offense results in increasingly positive results – some exponential function too complex for simple analysis and certainly beyond my ability to determine what that function is precisely, but looking over historical data, it certainly exists. In summary, two 30+ run guys hitting next to each other are, historically, worth more than 60 runs. Just scan stats from championship teams, look at a player’s stats when he was on a championship team versus when he was on not so successful team, and it becomes quite obvious quite quickly that productivity depends upon not only individual performance, but also teammates surrounding them – especially with offense.

gwangung on
January 6th, 2010 10:56 am

RBIs may be a poor measure of an individualâ€™s contribution, but it seems that the prima facie evidence is that it is a valid measure of the value of a batter in an offensive system â€“ the value of being surrounded by other productive offensive players.

This is the same, in a way, with whether or not a walk is worth more in a high run-scoring environment or a low one.

Arena-ball-era Coors Field: that baserunner is much more likely to score
Dodger Stadium: that baserunner is much more valuable, because they’re rarer

Your answer to that question turns out to answer a lot of related questions, including the compound offense one.

jld on
January 6th, 2010 11:01 am

I think there is probably some diminishing returns in terms of the value of offense and defense, not in terms of where it comes from.

Dave is right that it’s always better to have superior defenders vs inferior ones for any given position, but there are diminishing returns in terms of in game value. If you have 8 mythical defenders that make every out in their area, and you’re deciding to pick up a 9th, you probably won’t realize the same value as when you picked up the 3rd or 4th. Another way to say it is that going from a team that only allows 1 run per game to a team that allows .8 runs per game does not net many more wins.

It’s the same idea in offense. Having at team that scores 25 runs per game is not much better in practice than a team that scores 20 runs every game. Both will record wins in practically every game. Defensive diminishing returns exist in theory, but probably not in any realistic case.

The fact of the matter is that you want the best defender possible (based on availability, budget, value, etc) in every position, as well as the best batter possible in every spot in the line up.

wschroer on
January 6th, 2010 11:05 am

Itâ€™s the same idea in offense. Having at team that scores 25 runs per game is not much better in practice than a team that scores 20 runs every game. Both will record wins in practically every game.

I would agree with this premise, however the M’s, as currently constituted, will not have to worry about overproducing runs such that their offense is stronger than it really needs to be, and they are wasting runs when they could be using resources to further reduce the other team’s production. They are way way way down on the other end of the run production function curve.

I would think that the one reason a run scored is more important than a run saved is that at the end of the day you cant win a game 0 to -1. So surely a run scored at the point a game is tied with no score then that run scored eventually has more value â€“ doesnt it?

Well, until you can show us a team that’s already allowing 0.00 runs per game, I’m pretty sure additional defensive runs saved will always have just as much value as offensive runs added.

Even the best defensive/pitching teams still allow somewhere near 4 runs a game. You can always save runs by adding better defense.

jld on
January 6th, 2010 11:22 am

I would agree with this premise, however the Mâ€™s, as currently constituted, will not have to worry about overproducing runs such that their offense is stronger than it really needs to be, and they are wasting runs when they could be using resources to further reduce the other teamâ€™s production. They are way way way down on the other end of the run production function curve.

Yes, I think we’d all agree that the Ms do not currently have a problem with the overproduction of runs.

I’m just making a fringe case argument to show my point. The same dynamic would apply if you had a similar, mythically crazy defense.

Jeremariner on
January 6th, 2010 11:44 am

A penny saved is a penny earned, a run saved is a run earned. That’s the ultimate poor man’s logic, but the question I keep asking myself in regard to O vs D is, which situation does a position player find himself in more often during the course of a game: a run-scoring opportunity or a run-saving opportunity?

I think the fact that offensive production has accelerating returns is evident in the very nature of the traditional batting order: the guys who hit a lot of balls go right after the guys who hit a lot of bases. My evidence? Every lineup in baseball. If there wasn’t an accelerating return based on offensive balance, why would it matter who hit where?

I don’t know if a similar argument can be made for defense. I’m not saying it can’t be made, but I just don’t see it manifesting itself in such a clear way on the field of play. A 2b’s great throw can have a positive effect on a 1b’s catch, but then again, a consistently great thrower can also negate the need for a great catcher in the first place.

I’m just calling it as I see it. If that statement is good enough for an ump, it’s good enough for me. :p

FrankTheTank on
January 6th, 2010 11:49 am

Paul B, I misstated my point.

My thought is that at some point, defense has to be diminishing, since there are only so many runs that can be saved (in your example, the point where you get Supermen that can get to every ball not hit out of the park). The difference between getting to that point (whether that is possible or not), and getting to a point below that in terms is minimal. That is, your 9th Superman really didn’t add all that much, your 8 Supermen would have gotten to 99.9% of the balls anyway…

(You can adjust this for non-Supermen, assuming that only X% of hit balls are catchable by a team comprised of the best defenders at their positions in all baseball)

Now accepting that at some point (however far out you want to put it), defensive returns are diminishing, the question is whether our current defensive position is close enough to that point to have a diminishing effect.

I say it is. Dave (and you) seem to disagree.

Bluntly, I do not believe the necessary data exists to determine this and this remains more of a thought exercise than anything else. (that is, annecdotal UZR evidence is incomplete at best and irrelevant at worst)

Doing some playing with Pythag, and it looks like a small positive run differential is far more valuable to a team with great defense than to a team with poor defense. (The sword cuts both ways, though–a team with poor offense is hurt far more by a small negative run differential.)

I’ve put the semi-realistic range (based on last year’s actual min/max runs scored/runs allowed) in italics, but when I do that, it becomes pretty clear that we’re never, ever going to see a season where the “extreme endpoint” analyses suggested by prior commenters will have any relevance, and so in practice, a run saved will always be equal to a run scored.

Rodney on
January 6th, 2010 11:51 am

Put simply, almost every single ball in play that matters is only catchable by one player.

Infield groundouts require coordination between the infielder and the 1st baseman. It would seem to me that first base is the 1 position where there is a diminishing return on defense.

A first baseman who is adept at picking throws out of the dirt is more valuable to a team who throws a lot of balls in the dirt.

I don’t know enough about how defensive metrics are put together to know if picking throws out of the dirt is even a component of a first baseman’s defensive value, but whether it is or isn’t, I do think there is some diminishing return with regard to first baseman on any play where their play is combined with a throw from an infielder.

Also, when it comes to first base defense, picking throws in the dirt represent a significant amount of a first baseman’s defensive value.

Chris_From_Bothell on
January 6th, 2010 12:00 pm

Having a team that scores 25 runs per game is not much better in practice than a team that scores 20 runs every game.

Too extreme. More realistic: Is a team that scores that on paper scores 5 runs a game better than one that on paper scores 4 runs a game?

Given the streaky nature of offense, it’s hard to reliably construct a team that will win 4 runs or 5 runs a game. So you aim high and hope that over the course of a season the surges cancel the streaks. I.e. you aim for what should be a 5-run-per-game offense, hoping to see at least 4 runs a game when you factor in slumps and injuries.

brianf on
January 6th, 2010 12:05 pm

After reading the piece, I was going to make (though probably not as well) the argument that MFAN made above very well. My understanding of the math says he’s right, that you’ll have a mostly direct/linear impact on OBP, but surrendering runs is a different beast.

Another way of thinking of it–which was in my question for Saturday on that thread — is isn’t it significantly easier to reduce a run/game surrendered from 4->3, than from 2->1? There’s some exponent on run prevention math — because it’s clearly possible to squish from 5 to 4 runs a game, but is effectively impossible to go from 1 to 0 (or even 2 to 1)

If there wasnâ€™t an accelerating return based on offensive balance, why would it matter who hit where?

As it turns out, it doesn’t really matter who hits where. The difference between an optimal and pessimal lineup over 162 games is on the order of half a win

Chris_From_Bothell on
January 6th, 2010 12:12 pm

The difference between an optimal and pessimal lineup over 162 games is on the order of half a win

I’ll bear that in mind if I ever see a starting lineup for a game that has Rob Johnson batting first and Jack Wilson batting third.

wschroer on
January 6th, 2010 12:22 pm

As it turns out, it doesnâ€™t really matter who hits where. The difference between an optimal and pessimal lineup over 162 games is on the order of half a win

There is a principle in analysis that is usually called the reasonableness test, but is often also called the “stink” test. Simply put, does the analysis fit within reasonable analysis? If not, then likely your analysis is faulty.

In this case, whatever analysis you used is faulty.

This is exactly where such a worthless, lowdown, stupid, old school stat as RBI proves that batting orders matter. Rob Johnson hitting lead off is not nearly as effective a strategy as Ichiro hitting leadoff – and if your analysis does not point that out the fault is in your analysis.

@wschroer – Actually if you read “Baseball Between the Numbers: Why Everything You Know About the Game Is Wrong”, you’d find that Graham is right. If you took the same 9 players and rearranged them in any particular order, the difference is minimal.

Lots of things in life don’t pass the stink test, but are true. The human brain just isn’t optimized to think about certain problems the right way, so the answers seem wrong even when you can mathematically prove them to be true. The batting order is one instance, and the Monty Hall problem is another.

As long as those 3 are part of your best 9 OBP position players with at least some consideration given to defense and SLG, then sure I’d give it a whirl if nothing else than to test the theory IRL.

Heck, I’d even be willing to give the whole “pull lineups out of a hat” for 162 games a try as long as you have only the “best 9″ in the hat.

Chris_From_Bothell on
January 6th, 2010 1:15 pm

Kamina – See, that’s the thing. No real-life team is constructed that way. Almost no real-life team could be constructed that way, unless everyone’s OBP was roughly equivalent only because everyone’s OBP was replacement-level.

So as thought exercise, yes, lineup order doesn’t matter and there’s good math to show it. But you have to have certain pre-conditions for that to exist (everyone’s OBP pretty close to each other) that almost never come up.

LongTimeFan on
January 6th, 2010 1:17 pm

This is a really insightful post and one of the best in recent memory at taking an in depth look into the numbers behind baseball. There are a few things that I would like to add.

First, mfan has some very insightful analysis, but has overlooked a couple of things. Although the impact on runs saved would diminish as plus defenders are added to a team, the effect on added wins would not diminish so that there would not in fact be diminishing returns by continuing to upgrade the defense. (Example: although it is easier to reduce runs allowed from 3.5 per game to 3.0 than from 3.0 to 2.5, the added wins from going from 3.5 to 3.0 would be greatly exceeded by going from 3.0 to 2.5) Also, it must be pointed out that returns on offensive upgrades do not increase but actually stay constant the same as defensive upgrades. Sure, more runs are generated by adding a POINT of OBP to a high OBP team than to a low OBP team, but the effective runs added are greater when a high OBP PLAYER is added to a low OBP team because that PLAYER has a greater effect on the TEAM OBP and on TEAM runs on a low OBP team.

Secondly, I agree that defensive runs saved essentially are equal in value to offensive runs generated, but I would propose that there are several reasons why defensive upgrades may actually be better than offensive upgrades: 1) There is a greater likelihood that a terrific defender will have an above average year on offense than there is that a great offensive player will suddenly improve on defense, so the upside of a defensive player may be inherently higher all other things being equal. 2) The largely unquantifiable element in any game is errors and the better defensive team makes less of those which means that a great defensive team does not need to record an RBI in order to drive in the winning run, they just need to be better at defense than their opponent. You can in fact score runs on errors by the other team. 3) As stated earlier, better defensive teams experience less wear and tear on their pitchers throughout the season. 4) History has proven that you don’t need a great offense to win championships, but you do need a great defense. 5) Also as stated earlier, defense is cheaper than offense. This trade would essentially be a payroll swap with the money owed to Bill Hall going to Kotchman, which means that the team still should have about $8 to $10 million to invest in starting pitching and I am not quite convinced that we are done tinkering with 1st and 2nd base just yet.

I am very excited for 2010 and Jack Z may end up changing the way franchises look at building teams and the way defensive players are treated in the free agent market. Go Mariners!

FrankTheTank on
January 6th, 2010 2:38 pm

4) History has proven that you donâ€™t need a great offense to win championships, but you do need a great defense.

I’m sorry, this can’t go unchallenged.
I know the mantra “Defense Wins Championships” but besides the Ozzie Guillen’s go-go White Sox, who has won title recently without a superior offense?

(sorry for straying from this original topic, but I dislike claims like this…)

If these were my best 9, and if I understand the book correctly, then shoving Ichiro to the bottom of the lineup everyday might cost me 2 wins at most compared to lining them up in descending OBP order.

The players don’t have to be replacement-level or have similar OBP numbers for the theory to work though. At least that’s what I understood from reading it.

There is a greater likelihood that a terrific defender will have an above average year on offense than there is that a great offensive player will suddenly improve on defense

All the more reason to have multiple above-average hitters, because hitting is streaky and you need some insurance against one or two guys slumping. The 2009 Ms are a recent example of what can happen if you build for superior defense and superior pitching, and expect just average offense will be sufficient: good, but not great.

The 2009 Ms are a recent example of what can happen if you build for superior defense and superior pitching, and expect just average offense will be sufficient: good, but not great.

Superior defense, yes…
Average offense, sure…
Superior pitching… um….

Outside of King Felix, and the approximate Â½ seasons out of Washburn, that Canadian guy, and oh yeah RRS, 78 games were thrown by the likes of Vargas, Snell, Olson, Morrow, Jakubauskas, French, Fister and Silva (*shudder*).

The 2009 Ms are a recent example of what can happen if you build for superior defense and superior pitching, and expect just average offense will be sufficient: good, but not great.

Hmmm…

Superior defence – Yes! Definitely! Top UZR/150 in the league by a big margin!

Superior pitching – well, we only were better than 4 teams in the league in xFIP (Orioles, Indians, Rangers, and Angels) so low average at best – certainly not superior.

Average offense – well, our wOBA was the absolute worst in the league. Nuf said.

Luck in 1-run decisions (35-20) – Yes!

Results show 85 wins. It’s a good year.

wschroer on
January 6th, 2010 4:02 pm

Since 1972, there have been twenty-seven teams that made the postseason in spite of having below-average offenses. Of these, seven won the World Series: the 1985 Royals, 1987 Twins, 1990 Reds, 1995 Braves, 1996 Yankees, 2000 Yankees, and 2005 White Sox. All of these teams, except the 1987 Twins, had excellent pitching staffs; itâ€™s hard to make the playoffs with a below-average offense unless you have an excellent pitching staff.
Conversely, twenty teams have made the postseason with below-average run prevention. None of them won the World Series, and only two (the 1982 Brewers and 1993 Phillies) even played for the championship. Sixteen of the twenty lost the first playoff series in which they played.

This is interesting data, especially the conclusion. Even those teams you call out as WS champs which were inferior offensively, were not that far below average. And from my cursory look, none of them were Mariner-sized below average.

Certainly playoff teams can be built without screaming hot offenses, but that is not optimal – screaming hot offenses are generally going to be more successful given that the other phases of the game are not ignored.

History would say it is more likely that a team will make the playoffs due to good defense, good pitching and good offense rather than excellent defense, good pitching, and dreadful offense. Right now, we are a dreadful offense. In our case, it probably would not matter all that much if Ichiro did bat 7th, to tell you the truth.

Jeremariner on
January 6th, 2010 4:33 pm

Taking market value into consideration, I’ll gladly side with all of the defense-defenders here.

Throwing “diminished” value and “accelerating” value aside for a minute, offense and defense both have a lot of just plain value, obviously. And it is a lot easier to build a spectacular defensive 8-position roster on a ~$100M payroll than it is to build a spectacular 8/9-man lineup on the same payroll because the market value of defense is so disproportionately low.

It’s like buying 5 boxes of store brand cereal for the price of one name brand! (Breakfast of champions, anyone?)

And this, I think we can agree, is where Jack Z has been a true wizard. (or wizdurd?…)

wschroer on
January 6th, 2010 4:55 pm

Throwing â€œdiminishedâ€ value and â€œacceleratingâ€ value aside for a minute, offense and defense both have a lot of just plain value, obviously. And it is a lot easier to build a spectacular defensive 8-position roster on a ~$100M payroll than it is to build a spectacular 8/9-man lineup on the same payroll because the market value of defense is so disproportionately low.

I love going super economy when it comes to airline tickets, but not if it involves changing my destination from Hawaii to Pullman.

Chris_From_Bothell on
January 6th, 2010 5:03 pm

Kamina, georgmi, oolon – I said built for. You’re listing off the results. I’m talking about what was intended at the start of 2009.

The plan, going into 2009, was to expect average offense and have the pitching and defense be what really got the wins. When the offense fell off of a cliff and half the reliable starters in the rotation were traded away, the only things holding it together to get to a better than .500 season were luck (one-run games) and defense (top in the league).

85 wins. 12 more wins were needed to win the west, 10 more wins needed to win the wild card. Reduce that down to perhaps 10 and 9, respectively, if some of those wins were likely to have been against Anaheim or Boston. Could those 10 or so wins have come from improved #3 and #4 pitchers alone? Didn’t they need a better bat in there at some point?

jouish on
January 6th, 2010 5:21 pm

screaming hot offenses are generally going to be more successful given that the other phases of the game are not ignored.

Putting aside the fact that looking at WS teams to prove or disprove this argument is not probably the best method, you’re making relative arguments. An excellent defense would be consisted of a bunch of +10 defenders, while an excellent offense could consist of a bunch of +30 hitters.

There is no absolute difference between a group of 9 +10 defense/0 offense and a group of 0 defense/+10 offense.

LongTimeFan on
January 6th, 2010 5:35 pm

I know the mantra â€œDefense Wins Championshipsâ€ but besides the Ozzie Guillenâ€™s go-go White Sox, who has won title recently without a superior offense?

I’m not trying to say that it is easy to win a championship without a great offense, just that it is entirely necessary to have a great defense in order to win. The Mariners may not be likely to win the World Series this year, but they do have a great chance at contending for a playoff spot and then once you get in who knows?

Also, has anyone else noticed that by pursuing players with undervalued skill sets the Mariners are putting themselves in excellent position to be able to spend some serious money over the next two years in acquiring the two rarest commodities currently in baseball, namely dominant pitching and a power-hitting left handed 1st baseman? (I think we can all think of a couple of good candidates for those positions.)

Jeremariner on
January 6th, 2010 5:53 pm

I love going super economy when it comes to airline tickets, but not if it involves changing my destination from Hawaii to Pullman.

If you want to see a whole 25-man roster go to Hawaii first class, root for the Yankees.
I’ll be just fine in seat 27D eating my peanuts with all of the undervalued talent we’re getting on the cheap. There is more than one way to get to Hawaii, y’know.

I will, however, hold out hope that Jack Z can dig us up a real crown jewel: some undervalued offensive prowess. Ooooh, aaaah…

nathaniel dawson on
January 6th, 2010 6:17 pm

â€¦doesnâ€™t even mention that above average fielding at first base hides (or makes up for some) deficiencies elsewhere on the infield, and in fact makes them all better.

The reason here is that upgrading first base defense is the only position where upgrading improves the defense of more than one player, as improved 1B defense will affect all infielders performance. By upgrading to Kotchman, we improve the overall defense of the infield

Is there a quantified effect that a good defensive first baseman has on the defensive statistics of the other infield positions? My first thought is that an agile defensive first baseman would be a significant benefit to the other infielders by cutting down on the number of throwing errors assigned to them by picking balls or applying tags when pulled of the bag that average first baseman wouldnâ€™t make.

Could it not also be argued that adding a defensive specialist at first base would increase the defence of all the other players on the infield.
The reason being that say a shortstop for example would be more inclinded to make a difficult throw because he has faith that his first baseman would be able to bail him out if the throw went wild.

That being said, a good defensive 1B who can dig low throws out of the dirt could give us some good accelerated returnâ€¦

There’s no doubt that a firstbaemen that has great ability to scoop throws should have an positive impact on the other infielders. What I haven’t seen yet is whether or not Kotchman has that elevated level of ability. Has anybody seen evidence that he’s better able to handle throws from infielders such that we should assume he’s going to make our other infielders better?

nathaniel dawson on
January 6th, 2010 6:23 pm

Of course WAR relates to the number of wins on a team, because it is a derivative stat.

No, it’s not. Win Shares would be a derivitave stat, but WAR considers the events produced by the different players and contrasts them with league average to to arrive at a value. It does not consider team context and a team’s total WAR can often be different than it’s won/lost record.

nathaniel dawson on
January 6th, 2010 6:29 pm

As it turns out, it doesnâ€™t really matter who hits where. The difference between an optimal and pessimal lineup over 162 games is on the order of half a win.

I’m pretty sure that the difference between optimal and pessimal (nice word, by the way) is much more than that. I hadn’t previously seen the link Jeremariner provided that estimated it at 6 wins, but I’ve seen many other sims put it at around 3 or 4.

Whoops, you’re totally right. I should have said that the difference between optimal and MLB standard is around a half win, and then the drop to pessimal is another 2.5-3.5, which completely invalidates my point.

knuckleslurve on
January 6th, 2010 7:53 pm

Here’s why there is no minimum level of offense needed: Any time a team loses, it could’ve prevented the loss by not allowing their opponent as many runs as they did. The only scenario that could be claimed as an example of diminishing returns, where creating a more balanced roster could’ve won the game, is if a team loses a game that went into extra innings tied at zero. How many of those ever happen? If this happened a lot, it could be said that the team was already so good at preventing runs that they would’ve still shut out their opponent through nine even if they’d replaced one of their Adam Everetts with an Adam Dunn. Since this is an extreme, the minimum offense argument shouldn’t have any weight.

Alex on
January 6th, 2010 8:09 pm

I will, however, hold out hope that Jack Z can dig us up a real crown jewel: some undervalued offensive prowess. Ooooh, aaaahâ€¦

Milton Bradley.

Breadbaker on
January 6th, 2010 8:59 pm

Milton Bradley.

Insert mandatory “games” joke here. But seriously, anything one can buy with the coin of Carlos Silva is a win.

wschroer on
January 7th, 2010 12:20 am

If you want to see a whole 25-man roster go to Hawaii first class, root for the Yankees.

Unfortunately my friend, you may have been sold a plane ticket to Hawaii, but you are in fact on a slow bus to the bottom of the division.

One does not have to be in first class to compete and perhaps to win, but you do need to climb out of the luggage bins and stop digging around for quarters in the upholstery.

wschroer on
January 7th, 2010 12:30 am

[meta]

wschroer on
January 7th, 2010 12:38 am

Iâ€™m not trying to say that it is easy to win a championship without a great offense, just that it is entirely necessary to have a great defense in order to win

Huh? Since when? I will grant you that it is certainly easier to win when you have decent defense, but this years Yanks were not a particularly stunning model of defense. Even using the stats supposing to show the importance of defense, UZR, the Yanks were at -18 according to Fangraph, and as I recall, they won a little something called the World Series.

wschroer on
January 7th, 2010 12:51 am

[meta]

Jacobs on
January 14th, 2010 9:33 am

I’ve read both posts and comments and believe I’m not repeating anyone. I did not see much direct discussion of defensive positioning. Though this post has fallen off the front page, it’s very much worthy of further discussion.

First of all, proper defensive positioning justifies one of Dave’s main arguments. Dave claimed (obvious paraphrasing) that the number of extreme, high-impact plays that can be handled by more than one defender are very rare. I agree, because teams position their players expressly to avoid such overlapping coverage.

Positioning allows the addition of a good defender to not take away high-impact opportunities from neighboring players by adding range on the other side of the neighboring positions. Examples from obvious to less so:
(a) SS and 2B with extreme range allow 1B and 3B to shade towards the lines and take away doubles and triples. The inverse is also true.
(b) Infielders with extremely good range into the outfield on flyballs allow outfielders to play deeper and take away additional doubles and triples.
(c) CF with huge range allows LF and RF to take away flyballs down the line and extend their range into foul territory.
(d) 3B with extremely good bunt-charging skills (Beltre anyone?) allow C and P to ignore the 3B side on bunts and take away the first side. Perhaps 1B don’t need to charge at all in some circumstances.
(e) Slick SS and 2B encourage P to ignore all grounders except those hit pretty much at him.
(f) Extreme range 2B reduces the positioning “penalty” paid by holding runners at 1B.

In short, if clubs make adjustments to all defenders as better individuals are added to the defense, the added range shouldn’t take away from neighboring players. The biggest impact is reduction of extra-base hits along the lines and to the wall. Otherwise ignored opportunities are added, such as more range in foul territory.

jsolid on
January 24th, 2010 9:34 pm

i want to address what i feel are the two most germane questions raised so far.
one, does a run saved = a run scored ?
two, given a great defender, what specific benefit will he bring to your specific team ?

i had submitted a long post on this. it seems to have disappeared (arrgh), so i’ll sum up the major points.

one, using pythagoras calculations, a run saved does equal a run scored. this varies slightly the further from average a team is. comparing runs scored and runs allowed, for a team with around a +75 run differential, run saved have a 10% bonus. for a team with around a +175 differential, runs saved have a 20% bonus. for a team with a +300 differential, runs saved have a 30% bonus. conversely, for teams that give up more runs than they score, runs scored are worth slightly more, at similar rates.
i want to emphasize – since this is a common misconception – for a team that scores and allows about the same number of runs, a run scored = a run saved. it doesnt matter if the team scores and allows 600 runs, or scores and allows 1000 runs.

two, the actual (defensive) impact of a player for your team is hard to tell. a first baseman who is good at scooping throws is valuable if your infielders are wild throwers, but not if they arent. so without play-by-play analysis, you probably have to take the known defensive value then make an educated adjustment.